IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v417y2015icp176-184.html
   My bibliography  Save this article

The Hurst exponents of Nitzschia sp. diatom trajectories observed by light microscopy

Author

Listed:
  • Murguía, J.S.
  • Rosu, H.C.
  • Jimenez, A.
  • Gutiérrez-Medina, B.
  • García-Meza, J.V.

Abstract

We present the results of an experiment with light microscopy performed to capture the trajectories of live Nitzschia sp. diatoms. The time series corresponding to the motility of this kind of cells along ninety-five circular-like trajectories have been obtained and analyzed with the scaling statistical method of detrended fluctuation analysis optimized via a wavelet transform. In this way, we determined the Hurst parameters, in two orthogonal directions, which characterize the nature of the motion of live diatoms in light microscopy experiments. We have found mean values of these directional Hurst parameters between 0.70 and 0.63 with overall standard errors below 0.15. These numerical values give evidence that the motion of Nitzschia sp. diatoms is of persistent type and suggest an active cell motility with a kind of memory associated with long-range correlations on the path of their trajectories. For the collected statistics, we also find that the values of the Hurst exponents depend on the number of abrupt turns that occur in the diatom trajectory and on the type of wavelet, although their mean values do not change much.

Suggested Citation

  • Murguía, J.S. & Rosu, H.C. & Jimenez, A. & Gutiérrez-Medina, B. & García-Meza, J.V., 2015. "The Hurst exponents of Nitzschia sp. diatom trajectories observed by light microscopy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 176-184.
  • Handle: RePEc:eee:phsmap:v:417:y:2015:i:c:p:176-184
    DOI: 10.1016/j.physa.2014.09.046
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437114008140
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2014.09.046?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Murguía, J.S. & Rosu, H.C., 2012. "Multifractal analyses of row sum signals of elementary cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(13), pages 3638-3649.
    2. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    3. Nagarajan, Radhakrishnan & Kavasseri, Rajesh G., 2005. "Minimizing the effect of trends on detrended fluctuation analysis of long-range correlated noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 182-198.
    4. Liang Li & Simon F Nørrelykke & Edward C Cox, 2008. "Persistent Cell Motion in the Absence of External Signals: A Search Strategy for Eukaryotic Cells," PLOS ONE, Public Library of Science, vol. 3(5), pages 1-11, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vargas-Olmos, C. & Murguía, J.S. & Ramírez-Torres, M.T. & Mejía Carlos, M. & Rosu, H.C. & González-Aguilar, H., 2016. "Perceptual security of encrypted images based on wavelet scaling analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 22-30.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhao, Xiaojun & Shang, Pengjian & Zhao, Chuang & Wang, Jing & Tao, Rui, 2012. "Minimizing the trend effect on detrended cross-correlation analysis with empirical mode decomposition," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 166-173.
    2. Michalski, Sebastian, 2008. "Blocks adjustment—reduction of bias and variance of detrended fluctuation analysis using Monte Carlo simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 217-242.
    3. Vitanov, Nikolay K. & Hoffmann, Norbert P. & Wernitz, Boris, 2014. "Nonlinear time series analysis of vibration data from a friction brake: SSA, PCA, and MFDFA," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 90-99.
    4. Leonarduzzi, R. & Wendt, H. & Abry, P. & Jaffard, S. & Melot, C. & Roux, S.G. & Torres, M.E., 2016. "p-exponent and p-leaders, Part II: Multifractal analysis. Relations to detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 319-339.
    5. Nagarajan, Radhakrishnan, 2006. "Reliable scaling exponent estimation of long-range correlated noise in the presence of random spikes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 1-17.
    6. Vargas-Olmos, C. & Murguía, J.S. & Ramírez-Torres, M.T. & Mejía Carlos, M. & Rosu, H.C. & González-Aguilar, H., 2016. "Perceptual security of encrypted images based on wavelet scaling analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 22-30.
    7. Lavička, Hynek & Kracík, Jiří, 2020. "Fluctuation analysis of electric power loads in Europe: Correlation multifractality vs. Distribution function multifractality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    8. Priscila C A da Silva & Tiago V Rosembach & Anésia A Santos & Márcio S Rocha & Marcelo L Martins, 2014. "Normal and Tumoral Melanocytes Exhibit q-Gaussian Random Search Patterns," PLOS ONE, Public Library of Science, vol. 9(9), pages 1-13, September.
    9. Kakinaka, Shinji & Umeno, Ken, 2021. "Exploring asymmetric multifractal cross-correlations of price–volatility and asymmetric volatility dynamics in cryptocurrency markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    10. Longfeng Zhao & Wei Li & Andrea Fenu & Boris Podobnik & Yougui Wang & H. Eugene Stanley, 2017. "The q-dependent detrended cross-correlation analysis of stock market," Papers 1705.01406, arXiv.org, revised Jun 2017.
    11. Vitanov, Nikolay K. & Sakai, Kenshi & Dimitrova, Zlatinka I., 2008. "SSA, PCA, TDPSC, ACFA: Useful combination of methods for analysis of short and nonstationary time series," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 187-202.
    12. El Alaoui, Marwane & Benbachir, Saâd, 2013. "Multifractal detrended cross-correlation analysis in the MENA area," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5985-5993.
    13. Méndez-Gordillo, Alma Rosa & Cadenas, Erasmo, 2021. "Wind speed forecasting by the extraction of the multifractal patterns of time series through the multiplicative cascade technique," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    14. Nagarajan, Radhakrishnan & Kavasseri, Rajesh G., 2005. "Minimizing the effect of periodic and quasi-periodic trends in detrended fluctuation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 777-784.
    15. Diniz-Maganini, Natalia & Diniz, Eduardo H. & Rasheed, Abdul A., 2021. "Bitcoin’s price efficiency and safe haven properties during the COVID-19 pandemic: A comparison," Research in International Business and Finance, Elsevier, vol. 58(C).
    16. Mei, Dexiang & Liu, Jing & Ma, Feng & Chen, Wang, 2017. "Forecasting stock market volatility: Do realized skewness and kurtosis help?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 153-159.
    17. Zhang, Jiao & Li, Youping & Liu, Chunqiong & Wu, Bo & Shi, Kai, 2022. "A study of cross-correlations between PM2.5 and O3 based on Copula and Multifractal methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    18. Alvarez-Ramirez, Jose & Alvarez, Jesus & Rodriguez, Eduardo, 2008. "Short-term predictability of crude oil markets: A detrended fluctuation analysis approach," Energy Economics, Elsevier, vol. 30(5), pages 2645-2656, September.
    19. Yun-Jung Lee & Neung-Woo Kim & Ki-Hong Choi & Seong-Min Yoon, 2020. "Analysis of the Informational Efficiency of the EU Carbon Emission Trading Market: Asymmetric MF-DFA Approach," Energies, MDPI, vol. 13(9), pages 1-14, May.
    20. Li, Xing, 2021. "On the multifractal analysis of air quality index time series before and during COVID-19 partial lockdown: A case study of Shanghai, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:417:y:2015:i:c:p:176-184. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.